Question

Find the area of a triangle two sides of which are 8cm and 11cm and the perimeter is
32 cm.​

Answer 1

Step-by-step explanation:

Let a,b,c be the sides of the given triangle and 2s be its perimeter such that

a=8 cm, b=11 cm and 2s=32 cm

Now, a+b+c=2s

8+11+c=32

c=13

Therefore,

s−a=16−8=8,s−b=16−11=5,s−c=16−13=3

Hence, area of given triangle =

s(s−a)(s−b)(s−c)

=16×8×5×3

=8underoot30cm

Answer 2

Area Of Triangle = 43.8 cm²

Step-by-step explanation:

GIVEN

A = 8 cm

B = 11 cm

Perimeter = 32 cm

___________________________

TO FIND

Area Of Triangle

___________________________

We know that,

Perimeter Of Triangle = A + B + C

32 = 8 + 11 + C

32 = 19 + C

C = 32 - 19

C = 13

C = 13 cm

___________________________

We know that,

S = ( A + B + C ) / 2

S = ( 8 + 11 + 13 ) / 2

S = 32 / 2

S = 16

We know that,

Area Of Triangle = √{ s × ( s - a ) × ( s - b ) × ( s - c ) }

Area Of Triangle = √{ 16 × ( 16 - 8 ) × ( 16 - 11 ) × ( 16 - 11 ) }

Area Of Triangle = √{ 16 × 8 × 5 × 3 }

Area Of Triangle = √{ 16 × 120 )

Area Of Triangle = √1920

Area Of Triangle = 43.8

Area Of Triangle = 43.8 cm²